# Real constants and functions

Show how to use the following math constants and functions in your language   (if not available, note it):

Real constants and functions
You are encouraged to solve this task according to the task description, using any language you may know.
•   e   (base of the natural logarithm)
•   ${\displaystyle \pi}$
•   square root
•   logarithm   (any base allowed)
•   exponential   (ex )
•   absolute value   (a.k.a. "magnitude")
•   floor   (largest integer less than or equal to this number--not the same as truncate or int)
•   ceiling   (smallest integer not less than this number--not the same as round up)
•   power   (xy )

## 11l

Translation of: Python
math:e   // e
math:pi  // pi
sqrt(x)  // square root
log(x)   // natural logarithm
log10(x) // base 10 logarithm
exp(x)   // e raised to the power of x
abs(x)   // absolute value
floor(x) // floor
ceil(x)  // ceiling
x ^ y    // exponentiation

## 6502 Assembly

None of these are built-in, irrational constants are best implemented with lookup tables. Absolute value can be handled like so:

GetAbs: ;assumes value we want to abs() is loaded into accumulator
eor #$ff clc adc #1 rts ## ACL2 Only the last three are available as built in functions. (floor 15 2) ;; This is the floor of 15/2 (ceiling 15 2) (expt 15 2) ;; 15 squared  ==ACL2== Only the last three are available as built in functions. loor and ceiling are not provided, one can define them using integer part: define floor(x); if x < 0 then -intof(x); else intof(x); endif; enddefine; define ceiling(x); -floor(-x); enddefine; ## Action! Part of the solution can be find in REALMATH.ACT. INCLUDE "H6:REALMATH.ACT" PROC Euler(REAL POINTER e) REAL x IntToReal(1,x) Exp(x,e) RETURN PROC Main() REAL a,b,c INT i Put(125) PutE() ;clear screen MathInit() Euler(a) Print("e=") PrintR(a) PrintE(" by Exp(1)") ValR("2",a) Sqrt(a,b) Print("Sqrt(") PrintR(a) Print(")=") PrintR(b) Print(" by Power(") PrintR(a) PrintE(",0.5)") ValR("2.5",a) Ln(a,b) Print("Ln(") PrintR(a) Print(")=") PrintRE(b) ValR("14.2",a) Log10(a,b) Print("Log10(") PrintR(a) Print(")=") PrintRE(b) ValR("-3.7",a) Exp(a,b) Print("Exp(") PrintR(a) Print(")=") PrintRE(b) ValR("2.6",a) Exp10(a,b) Print("Exp10(") PrintR(a) Print(")=") PrintRE(b) ValR("25.3",a) ValR("1.3",b) Power(a,b,c) Print("Power(") PrintR(a) Print(",") PrintR(b) Print(")=") PrintRE(c) ValR("-32.5",a) RealAbs(a,b) Print("Abs(") PrintR(a) Print(")=") PrintR(b) PrintE(" by bit manipulation") ValR("23.15",a) i=Floor(a) Print("Floor(") PrintR(a) PrintF(")=%I by own function%E",i) ValR("-23.15",a) i=Floor(a) Print("Floor(") PrintR(a) PrintF(")=%I by own function%E",i) ValR("23.15",a) i=Ceiling(a) Print("Ceiling(") PrintR(a) PrintF(")=%I by own function%E",i) ValR("-23.15",a) i=Ceiling(a) Print("Ceiling(") PrintR(a) PrintF(")=%I by own function%E",i) PutE() PrintE("There is no support in Action! for pi.") RETURN Output: e=2.71828179 by Exp(1) Sqrt(2)=1.41421355 by Power(2,0.5) Ln(2.5)=.9162907319 Log10(14.2)=1.15228834 Exp(-3.7)=.0247235365 Exp10(2.6)=398.106988 Power(25.3,1.3)=66.6893784 Abs(-32.5)=32.5 by bit manipulation Floor(23.15)=23 by own function Floor(-23.15)=-24 by own function Ceiling(23.15)=24 by own function Ceiling(-23.15)=-23 by own function There is no support in Action! for pi.  ## ActionScript Actionscript has all the functions and constants mentioned in the task, available in the Math class. Math.E; //e Math.PI; //pi Math.sqrt(u); //square root of u Math.log(u); //natural logarithm of u Math.exp(u); //e to the power of u Math.abs(u); //absolute value of u Math.floor(u);//floor of u Math.ceil(u); //ceiling of u Math.pow(u,v);//u to the power of v  The Math class also contains several other constants. Math.LN10; // natural logarithm of 10 Math.LN2; // natural logarithm of 2 Math.LOG10E; // base-10 logarithm of e Math.LOG2E; // base-2 logarithm of e Math.SQRT1_2;// square root of 1/2 Math.SQRT2; //square root of 2  ## Ada Most of the constants and functions used in this task are defined in the pre-defined Ada package Ada.Numerics.Elementary_Functions. Ada.Numerics.e -- Euler's number Ada.Numerics.pi -- pi sqrt(x) -- square root log(x, base) -- logarithm to any specified base exp(x) -- exponential abs(x) -- absolute value S'floor(x) -- Produces the floor of an instance of subtype S S'ceiling(x) -- Produces the ceiling of an instance of subtype S x**y -- x raised to the y power  ## Aime # e exp(1); # pi 2 * asin(1); sqrt(x); log(x); exp(x); fabs(x); floor(x); ceil(x); pow(x, y); ## ALGOL 68 REAL x:=exp(1), y:=4*atan(1); printf(($g(-8,5)"; "$, exp(1), # e # pi, # pi # sqrt(x), # square root # log(x), # logarithm base 10 # ln(x), # natural logarithm # exp(x), # exponential # ABS x, # absolute value # ENTIER x, # floor # -ENTIER -x, # ceiling # x ** y # power # )) Output:  2.71828; 3.14159; 1.64872; 0.43429; 1.00000; 15.15426; 2.71828; 2.00000; 3.00000; 23.14069;  ALGOL 68 also includes assorted long, short and complex versions of the above, eg: long exp, long long exp, short exp, complex exp etc. And assorted trig functions: sin(x), arcsin(x), cos(x), arccos(x), tan(x), arctan(x), arctan2(x,y), sinh(x), arcsinh(x), cosh(x), arccosh(x), tanh(x) AND arctanh(x). ## ALGOL W begin real t, u; t := 10; u := -2.3; i_w := 4; s_w := 0; r_format := "A"; r_d := 4; r_w := 9; % set output format % write( " e: ", exp( 1 ) ); % e % write( " pi: ", pi ); % pi % write( " root t: ", sqrt( t ) ); % square root % write( " log t: ", log( t ) ); % log base 10 % write( " ln t: ", ln( t ) ); % log base e % write( " exp u: ", exp( u ) ); % exponential % write( " abs u: ", abs u ); % absolute value % write( " floor pi: ", entier( pi ) ); % floor % write( "ceiling pi: ", - entier( - pi ) ); % ceiling % % the raise-to-the-power operator is "**" - it only allows integers for the power % write( " pi cubed: ", pi ** 3 ) % use exp( ln( x ) * y ) for general x^y % end. ## ARM Assembly /* functions not availables */  ## Arturo print ["Euler:" e] print ["Pi:" pi] print ["sqrt 2.0:" sqrt 2.0] print ["ln 100:" ln 100] print ["log(10) 100:" log 100 10] print ["exp 3:" exp 3] print ["abs -1:" abs neg 1] print ["floor 23.536:" floor 23.536] print ["ceil 23.536:" ceil 23.536] print ["2 ^ 8:" 2 ^ 8]  Output: Euler: 2.718281828459045 Pi: 3.141592653589793 sqrt 2.0: 1.414213562373095 ln 100: 4.605170185988092 log(10) 100: 2.0 exp 3: 20.08553692318767 abs -1: 1 floor 23.536: 23 ceil 23.536: 24 2 ^ 8: 256 ## Asymptote real e = exp(1); // e not available write("e = ", e); write("pi = ", pi); real x = 12.345; real y = 1.23; write("sqrt = ", sqrt(2)); // square root write("ln = ", log(e)); // natural logarithm base e write("log = ", log10(x)); // base 10 logarithm write("log1p = ", log1p(x)); // log (1+x) write("exp = ", exp(e)); // exponential write("abs = ", abs(-1)); // absolute value write("fabs = ", fabs(-1)); // absolute value write("floor = ", floor(-e)); // floor write("ceil = ", ceil(-e)); // ceiling write("power = ", x ^ y); // power write("power = ", x ** y); // power  Output: e = 2.71828182845905 pi = 3.14159265358979 sqrt = 1.4142135623731 ln = 1 log = 1.09149109426795 log1p = 2.59114178285649 exp = 15.1542622414793 abs = 1 fabs = 1 floor = -3 ceil = -2 power = 22.0056421323763 power = 22.0056421323763 ## AutoHotkey The following math functions are built into AutoHotkey: Sqrt(Number) ; square root Log(Number) ; logarithm (base 10) Ln(Number) ; natural logarithm (base e) Exp(N) ; e to the power N Abs(Number) ; absolute value Floor(Number) ; floor Ceil(Number) ; ceiling x**y ; x to the power y  No mathematical constants are built-in, but they can all be calculated: e:=exp(1) pi:=2*asin(1)  The following are additional trigonometric functions that are built into the AutoHotkey language: Sin(Number) ; sine Cos(Number) ; cosine Tan(Number) ; tangent ASin(Number) ; arcsine ACos(Number) ; arccosine ATan(Number) ; arctangent  ## AWK Awk has square root, logarithm, exponential and power. BEGIN { print sqrt(2) # square root print log(2) # logarithm base e print exp(2) # exponential print 2 ^ -3.4 # power } # outputs 1.41421, 0.693147, 7.38906, 0.0947323  Power's note: With nawk or gawk, 2 ** -3.4 acts like 2 ^ -3.4. With mawk, 2 ** -3.4 is a syntax error. Nawk allows **, but its manual page only has ^. Gawk's manual warns, "The POSIX standard only specifies the use of ^' for exponentiation. For maximum portability, do not use the **' operator." Awk misses e, pi, absolute value, floor and ceiling; but these are all easy to implement: BEGIN { E = exp(1) PI = atan2(0, -1) } function abs(x) { return x < 0 ? -x : x } function floor(x) { y = int(x) return y > x ? y - 1 : y } function ceil(x) { y = int(x) return y < x ? y + 1 : y } BEGIN { print E print PI print abs(-3.4) # absolute value print floor(-3.4) # floor print ceil(-3.4) # ceiling } # outputs 2.71828, 3.14159, 3.4, -4, -3  ## Axe In general, Axe does not support many operations on real numbers. However, there are a few special cases that it does support. To take the square root of an integer X: √(X) To take the square root of an 8.8 fixed-point number Y: √(Y)ʳ To take the base-2 logarithm of an integer X: ln(X) To take 2 raised to an integer X: (Note that the base is not Euler's number) e^(X) To take the absolute value of a signed integer X: abs(X) ## BASIC Works with: QuickBasic version 4.5 abs(x) 'absolute value sqr(x) 'square root exp(x) 'exponential log(x) 'natural logarithm x ^ y 'power 'floor, ceiling, e, and pi not available  ### IS-BASIC 100 LET X=2:LET Y=5 110 PRINT EXP(1) ! value of e 120 PRINT PI ! value of Pi 130 PRINT ROUND(PI,3) ! rounds Pi to 3 decimal places 140 PRINT TRUNCATE(PI,3) ! cuts 3 decimal places from Pi 150 PRINT SQR(X) ! square root of x 160 PRINT LOG(X) ! the natural logarithm of number x 170 PRINT LOG2(X) ! logarithm of x to base 2 180 PRINT LOG10(X) ! logarithm of x to base 10 190 PRINT EXP(X) ! exponential 200 PRINT ABS(X) ! the absolute value of a number 210 PRINT INT(X) ! the largest whole number not bigger than x 220 PRINT IP(X) ! the integer part of x 230 PRINT FP(X) ! stands for fractorial part 240 PRINT CEIL(X) ! ceiling: gives the smallest whole number not less than x 250 PRINT X^Y ! power 260 PRINT MIN(X,Y) ! the smaller number of x and y 270 PRINT MAX(X,Y) ! the bigger number of x and y 280 PRINT EPS(X) ! the smallest quantity that can be added to or subtracted from x to make the interpreter register a change in the value of x 290 PRINT INF ! The largest positive number the tinterpreter can handle. This number is 9.999999999*10^62 ### Sinclair ZX81 BASIC Arguments to built-in functions may be placed in parentheses, but are not required to be. Base of the natural logarithm: EXP 1  ${\displaystyle \pi}$ : PI  Square root: SQR X  Natural logarithm: LN X  Exponential: EXP X  Absolute value: ABS X  Floor: INT X  (NB. Although this function is called INT, it corresponds to floor: e.g. INT -3.1 returns -4 not -3.) Ceiling: not provided as a built-in function. Power: X**Y  NB. Both ${\displaystyle x}$ and ${\displaystyle y}$ can be real numbers. ### BBC BASIC  e = EXP(1) Pi = PI Sqr2 = SQR(2) Ln2 = LN(2) Log2 = LOG(2) : REM Base 10 Exp2 = EXP(2) Abs2 = ABS(-2) Floor = INT(1.234) Ceil = FNceil(1.234) Power = 1.23^4 END DEF FNceil(n) = INT(n) - (INT(n) <> n)  ## BASIC256 e = exp(1) # e not available print "e = "; e print "PI = "; PI x = 12.345 y = 1.23 print "sqrt = "; sqr(x) # square root print "ln = "; log(e) # natural logarithm base e print "log10 = "; log10(e) # base 10 logarithm print "log = "; log(x)/log(y) # arbitrary base logarithm print "exp = "; exp(e) # exponential print "abs = "; abs(-1) # absolute value print "floor = "; floor(-e) # floor print "ceil = "; ceil(-e) # ceiling print "power = "; x ^ y # power Output: e = 2.71828182846 PI = 3.14159265359 sqrt = 3.51354521815 ln = 1.0 log10 = 0.4342944819 log = 12.1404787425 exp = 15.1542622415 abs = 1 floor = -3 ceil = -2 power = 22.0056421324 ## bc The language has square root and power, but power only works if the exponent is an integer. scale = 6 sqrt(2) /* 1.414213 square root */ 4.3 ^ -2 /* .054083 power (integer exponent) */  The standard library has natural logarithm and exponential functions. It can calculate e and pi: e comes from the exponential function, while pi is four times the arctangent of one. The usual formulas can calculate the powers with fractional exponents, and the logarithms with any base. Library: bc -l scale = 6 l(2) /* .693147 natural logarithm */ e(2) /* 7.389056 exponential */ p = 4 * a(1) e = e(1) p /* 3.141592 pi to 6 fractional digits */ e /* 2.178281 e to 6 fractional digits */ e(l(2) * -3.4) /* .094734 2 to the power of -3.4 */ l(1024) / l(2) /* 10.000001 logarithm base 2 of 1024 */  The missing functions are absolute value, floor and ceiling. You can implement these functions, if you know what to do. Translation of: AWK /* absolute value */ define v(x) { if (x < 0) return (-x) return (x) } /* floor */ define f(x) { auto s, y s = scale scale = 0 y = x / 1 scale = s if (y > x) return (y - 1) return (y) } /* ceiling */ define g(x) { auto s, y s = scale scale = 0 y = x / 1 scale = s if (y < x) return (y + 1) return (y) } v(-3.4) /* 3.4 absolute value */ f(-3.4) /* -4 floor */ g(-3.4) /* -3 ceiling */  ## blz The constant e {e} The constant pi {pi} Square root x ** 0.5 Logarithm (base n) x __ n Exponential {e} ** x Absolute Value abs(x) Floor floor(x) Ceiling ceil(x) Power x to the y x ** y ## BQN BQN has all the required constants, either within functions or available as single symbols:  ⋆1 # e and e^x 2.718281828459045 π # pi 3.141592653589793 √2 # square root 1.414213562373095 2⋆⁼10 # logarithm base n (inverse power) 3.321928094887363 |-1 # absolute value 1 ⌊3.2 # floor 3 ⌈3.2 # ceiling 4 3⋆4 # power 81 ## Bracmat Bracmat has no real number type, but the constants e and pi, together with i can be used as symbols with the intended mathematical meaning in exponential functions. For example, differentiation 10^x to x x \D (10^x) { \D is the differentiation operator } has the result 10^x*e\L10 { \L is the logarithm operator } Likewise e^(i*pi) evaluates to -1 and e^(1/2*i*pi) evaluates to i. When taking the square root of a (rational) number, and nominator and denominator are not too big (convertible to 32 or 64 bit integers, depending on platform), Bracmat resolves the number in prime factors and halves the exponents of each of the prime factors. Bracmat handles logarithms in any base, except real numbers that are not rational. Example: 24/7 \L 119/9 evaluates to 2+24/7\L5831/5184. Bracmat does not attempt to compute the numerical value of the exponential function, except for a the special case where the result is a rational number. Thus e^0 evaluates to 1. Bracmat has no built-in functions for computing the absolute value, floor or ceiling. For real numbers that are rational such functions can be written. If the result of taking the power of a rational number to another rational number is rational, Bracmat can in many compute it, if needed using prime factorization. See root above. Example:  243/1024^2/5 evaluates to 9/16. ## C Most of the following functions take a double. #include <math.h> M_E; /* e - not standard but offered by most implementations */ M_PI; /* pi - not standard but offered by most implementations */ sqrt(x); /* square root--cube root also available in C99 (cbrt) */ log(x); /* natural logarithm--log base 10 also available (log10) */ exp(x); /* exponential */ abs(x); /* absolute value (for integers) */ fabs(x); /* absolute value (for doubles) */ floor(x); /* floor */ ceil(x); /* ceiling */ pow(x,y); /* power */  To access the M_PI, etc. constants in Visual Studio, you may need to add the line #define _USE_MATH_DEFINES before the #include <math.h>. ## C# using System; class Program { static void Main(string[] args) { Console.WriteLine(Math.E); //E Console.WriteLine(Math.PI); //PI Console.WriteLine(Math.Sqrt(10)); //Square Root Console.WriteLine(Math.Log(10)); // Logarithm Console.WriteLine(Math.Log10(10)); // Base 10 Logarithm Console.WriteLine(Math.Exp(10)); // Exponential Console.WriteLine(Math.Abs(10)); //Absolute value Console.WriteLine(Math.Floor(10.0)); //Floor Console.WriteLine(Math.Ceiling(10.0)); //Ceiling Console.WriteLine(Math.Pow(2, 5)); // Exponentiation } }  ## C++ ### using Math macros #include <iostream> #include <cmath> #ifdef M_E static double euler_e = M_E; #else static double euler_e = std::exp(1); // standard fallback #endif #ifdef M_PI static double pi = M_PI; #else static double pi = std::acos(-1); #endif int main() { std::cout << "e = " << euler_e << "\npi = " << pi << "\nsqrt(2) = " << std::sqrt(2.0) << "\nln(e) = " << std::log(euler_e) << "\nlg(100) = " << std::log10(100.0) << "\nexp(3) = " << std::exp(3.0) << "\n|-4.5| = " << std::abs(-4.5) // or std::fabs(-4.5); both work in C++ << "\nfloor(4.5) = " << std::floor(4.5) << "\nceiling(4.5) = " << std::ceil(4.5) << "\npi^2 = " << std::pow(pi,2.0) << std::endl; }  ### using Boost Library: Boost #include <iostream> #include <iomanip> #include <cmath> #include <boost/math/constants/constants.hpp> int main() { using namespace boost::math::double_constants; std::cout << "e = " << std::setprecision(18) << e << "\ne³ = " << std::exp(3.0) << "\nπ = " << pi << "\nπ² = " << pi_sqr << "\n√2 = " << root_two << "\nln(e) = " << std::log(e) << "\nlg(100) = " << std::log10(100.0) << "\n|-4.5| = " << std::abs(-4.5) << "\nfloor(4.5) = " << std::floor(4.5) << "\nceiling(4.5) = " << std::ceil(4.5) << std::endl; }  Output: e = 2.71828182845904509 e³ = 20.0855369231876679 π = 3.14159265358979312 π² = 9.86960440108935799 √2 = 1.41421356237309515 ln(e) = 1 lg(100) = 2 |-4.5| = 4.5 floor(4.5) = 4 ceiling(4.5) = 5 ## Chef See Basic integer arithmetic#Chef for powers. ## Clojure Translation of: Java which is directly available. (Math/E); //e (Math/PI); //pi (Math/sqrt x); //square root--cube root also available (cbrt) (Math/log x); //natural logarithm--log base 10 also available (log10) (Math/exp x); //exponential (Math/abs x); //absolute value (Math/floor x); //floor (Math/ceil x); //ceiling (Math/pow x y); //power  Clojure does provide arbitrary precision versions as well: (ns user (:require [clojure.contrib.math :as math])) (math/sqrt x) (math/abs x) (math/floor x) (math/ceil x) (math/expt x y)  .. and as multimethods that can be defined for any type (e.g. complex numbers). (ns user (:require [clojure.contrib.generic.math-functions :as generic])) (generic/sqrt x) (generic/log x) (generic/exp x) (generic/abs x) (generic/floor x) (generic/ceil x) (generic/pow x y)  ## COBOL Everything that follows can take any number (except for SQRT which expects a non-negative number). The task constants and (intrinsic) functions: E *> e PI *> Pi SQRT(n) *> Sqaure root LOG(n) *> Natural logarithm LOG10(n) *> Logarithm (base 10) EXP(n) *> e to the nth power ABS(n) *> Absolute value INTEGER(n) *> While not a proper floor function, it is implemented in the same way. *> There is no ceiling function. However, it could be implemented like so: ADD 1 TO N MOVE INTEGER(N) TO Result *> There is no pow function, although the COMPUTE verb does have an exponention operator. COMPUTE Result = N ** 2  COBOL also has the following extra mathematical functions: FACTORIAL(n) *> Factorial EXP10(n) *> 10 to the nth power *> Trigonometric functions, including inverse ones, named as would be expected.  ## Common Lisp In Lisp we should really be talking about numbers rather than the type real. The types real and complex are subtypes of number. Math operations that accept or produce complex numbers generally do. (exp 1) ; e (Euler's number) pi ; pi constant (sqrt x) ; square root: works for negative reals and complex (log x) ; natural logarithm: works for negative reals and complex (log x 10) ; logarithm base 10 (exp x) ; exponential (abs x) ; absolute value: result exact if input exact: (abs -1/3) -> 1/3. (floor x) ; floor: restricted to real, two valued (second value gives residue) (ceiling x) ; ceiling: restricted to real, two valued (second value gives residue) (expt x y) ; power  ## Crystal x = 3.25 y = 4 puts x.abs # absolute value puts x.floor # floor puts x.ceil # ceiling puts x ** y # power puts include Math # without including puts E # puts Math::E -- exponential constant puts PI # puts Math::PI -- Archimedes circle constant puts TAU # puts Math::TAU -- the correct circle constant, >= version 0.36 puts sqrt(x) # puts Math.sqrt(x) -- real square root puts log(x) # puts Math.log(x) -- natural logarithm puts log10(x) # puts Math.log10(x) -- base 10 logarithm puts log(x, y) # puts Math.log(x, y) -- logarithm x base y puts exp(x) # puts Math.exp(x) -- exponential puts E**x # puts Math::E**x -- same  Template:0ut 3.25 3.0 4.0 111.56640625 2.718281828459045 3.141592653589793 6.283185307179586 1.8027756377319946 1.1786549963416462 0.5118833609788744 0.8502198590705461 25.790339917193062 25.79033991719306  ## D import std.math ; // need to import this module E // Euler's number PI // pi constant sqrt(x) // square root log(x) // natural logarithm log10(x) // logarithm base 10 log2(x) // logarithm base 2 exp(x) // exponential abs(x) // absolute value (= magnitude for complex) floor(x) // floor ceil(x) // ceiling pow(x,y) // power  ## Delphi Delphi supports all basic Standard Pascal (ISO 7185) functions shown in § Pascal. Furthermore, the following is possible, too: Pi; // π (Pi) LogN(BASE, x) // log of x for a specified base Log2(x) // log of x for base 2 Log10(x) // log of x for base 10 Floor(x); // floor Ceil(x); // ceiling Power(x, y); // power  Note, Log, Floor, Ceil and Power are from the Math unit, which needs to be listed in the uses-clauses. ## DWScript See Delphi. ## E ? 1.0.exp() # value: 2.7182818284590455 ? 0.0.acos() * 2 # value: 3.141592653589793 ? 2.0.sqrt() # value: 1.4142135623730951 ? 2.0.log() # value: 0.6931471805599453 ? 5.0.exp() # value: 148.4131591025766 ? (-5).abs() # value: 5 ? 1.2.floor() # value: 1 ? 1.2.ceil() # value: 2 ? 10 ** 6 # value: 1000000 ## EasyLang EasyLang does not have e, exponential, or a ceiling function. pi # Pi sqrt x # Square root logn x # Natural logarithm (base e) abs x # Absolute value floor x # Floor pow x y # Power ## Elena ELENA 4.x : import system'math; import extensions; public program() { console.printLine(E_value); //E console.printLine(Pi_value); //PI console.printLine(10.sqrt()); //Square Root console.printLine(10.ln()); //Logarithm console.printLine(10.log10()); // Base 10 Logarithm console.printLine(10.exp()); //Exponential console.printLine(10.Absolute); //Absolute value console.printLine(10.0r.floor()); //Floor console.printLine(10.0r.ceil()); //Ceiling console.printLine(2.power(5)); //Exponentiation } ## Elixir defmodule Real_constants_and_functions do def main do IO.puts :math.exp(1) # e IO.puts :math.pi # pi IO.puts :math.sqrt(16) # square root IO.puts :math.log(10) # natural logarithm IO.puts :math.log10(10) # base 10 logarithm IO.puts :math.exp(2) # e raised to the power of x IO.puts abs(-2.24) # absolute value IO.puts Float.floor(3.1423) # floor IO.puts Float.ceil(20.125) # ceiling IO.puts :math.pow(3,2) # exponentiation end end Real_constants_and_functions.main  ## Elm The following are all in the Basics module, which is imported by default: e -- e pi -- pi sqrt x -- square root logBase 3 9 -- logarithm (any base) e^x -- exponential abs x -- absolute value floor x -- floor ceiling x -- ceiling 2 ^ 3 -- power  ## Erlang % Implemented by Arjun Sunel -module(math_constants). -export([main/0]). main() -> io:format("~p~n", [math:exp(1)] ), % e io:format("~p~n", [math:pi()] ), % pi io:format("~p~n", [math:sqrt(16)] ), % square root io:format("~p~n", [math:log(10)] ), % natural logarithm io:format("~p~n", [math:log10(10)] ), % base 10 logarithm io:format("~p~n", [math:exp(2)] ), % e raised to the power of x io:format("~p~n", [abs(-2.24)] ), % absolute value io:format("~p~n", [floor(3.1423)] ), % floor io:format("~p~n", [ceil(20.125)] ), % ceiling io:format("~p~n", [math:pow(3,2)] ). % exponentiation floor(X) when X < 0 -> T = trunc(X), case X - T == 0 of true -> T; false -> T - 1 end; floor(X) -> trunc(X). ceil(X) when X < 0 -> trunc(X); ceil(X) -> T = trunc(X), case X - T == 0 of true -> T; false -> T + 1 end.  Output: 2.718281828459045 3.141592653589793 4.0 2.302585092994046 1.0 7.38905609893065 2.24 3 21 9.0 ok  ## ERRE PROGRAM R_C_F FUNCTION CEILING(X) CEILING=INT(X)-(X-INT(X)>0) END FUNCTION FUNCTION FLOOR(X) FLOOR=INT(X) END FUNCTION BEGIN PRINT(EXP(1)) ! e not available PRINT(π) ! pi is available or .... PRINT(4*ATN(1)) ! .... equal to X=12.345 Y=1.23 PRINT(SQR(X),X^0.5) ! square root PRINT(LOG(X)) ! natural logarithm base e PRINT(LOG(X)/LOG(10)) ! base 10 logarithm PRINT(LOG(X)/LOG(Y)) ! arbitrary base logarithm (y>0) PRINT(EXP(X)) ! exponential PRINT(ABS(X)) ! absolute value PRINT(FLOOR(X)) ! floor PRINT(CEILING(X)) ! ceiling PRINT(X^Y) ! power END PROGRAM Output:  2.718282 3.141592653589793 3.141593 3.513545 3.513545 2.513251 1.091491 12.14048 229808.1 12.345 12 13 22.00564 ## F# Translation of: C# – C sharp open System let main _ = Console.WriteLine(Math.E); // e Console.WriteLine(Math.PI); // Pi Console.WriteLine(Math.Sqrt(10.0)); // Square Root Console.WriteLine(Math.Log(10.0)); // Logarithm Console.WriteLine(Math.Log10(10.0)); // Base 10 Logarithm Console.WriteLine(Math.Exp(10.0)); // Exponential Console.WriteLine(Math.Abs(10)); // Absolute value Console.WriteLine(Math.Floor(10.0)); // Floor Console.WriteLine(Math.Ceiling(10.0)); // Ceiling Console.WriteLine(Math.Pow(2.0, 5.0)); // Exponentiation 0  ## Factor e ! e pi ! π sqrt ! square root log ! natural logarithm exp ! exponentiation abs ! absolute value floor ! greatest whole number smaller than or equal ceiling ! smallest whole number greater than or equal truncate ! remove the fractional part (i.e. round towards 0) round ! round to next whole number ^ ! power  ## Fantom The Float class holds 64-bit floating point numbers, and contains most of the useful mathematical functions. A floating point number must be specified when entered with the suffix 'f', e.g. 9f Float.e Float.pi 9f.sqrt 9f.log // natural logarithm 9f.log10 // logarithm to base 10 9f.exp // exponentiation (-3f).abs // absolute value, note bracket 3.2f.floor // nearest Int smaller than this number 3.2f.ceil // nearest Int bigger than this number 3.2f.round // nearest Int 3f.pow(2f) // power Note, . binds more tightly than -, so use brackets around negative numbers: > -3f.pow(2f) -9 > (-3f).pow(2f) 9  ## Forth 1e fexp fconstant e 0e facos 2e f* fconstant pi \ predefined in gforth fsqrt ( f -- f ) fln ( f -- f ) \ flog for base 10 fexp ( f -- f ) fabs ( f -- f ) floor ( f -- f ) \ round towards -inf : ceil ( f -- f ) fnegate floor fnegate ; \ not standard, though fround is available f** ( f e -- f^e )  ## Fortran  e ! Not available. Can be calculated EXP(1.0) pi ! Not available. Can be calculated 4.0*ATAN(1.0) SQRT(x) ! square root LOG(x) ! natural logarithm LOG10(x) ! logarithm to base 10 EXP(x) ! exponential ABS(x) ! absolute value FLOOR(x) ! floor - Fortran 90 or later only CEILING(x) ! ceiling - Fortran 90 or later only x**y ! x raised to the y power  4*ATAN(1.0) will be calculated in single precision, likewise EXP(1.0) (not EXP(1), because 1 is an integer) and although double precision functions can be named explicitly, 4*DATAN(1.0) will be rejected because 1.0 is in single precision and DATAN expects double. Thus, 4*DATAN(1.0D0) or 4*DATAN(1D0) will do, as the D in the exponent form specifies double precision. Whereupon, the generic names can be returned to: 4*ATAN(1D0). Some systems go further and offer quadruple precision. Others allow that all constants will be deemed double precision as a compiler option. The 4 need not be named as 4.0, or 4D0, as 4 the integer will be converted by the compiler to double precision, because it is to meet a known double precision value in simple multiplication and so will be promoted. Hopefully, at compile time. ## FreeBASIC ' FB 1.05.0 Win64 #Include "crt/math.bi" Print M_E '' constant "e" from C runtime library Print M_PI '' constant "pi" from C runtime library Print Sqr(2) '' square root function built into FB Print Log(M_E) '' log to base "e" built into FB Print log10(10) '' log to base 10 from C runtime library Print Exp(1) '' exponential function built into FB Print Abs(-1) '' absolute value function (integers or floats) built into FB Print Int(-2.5) '' floor function built into FB Print ceil(-2.5) '' ceiling function from C runtime library Print 2.5 ^ 3.5 '' exponentiation operator built into FB Sleep  Output:  2.718281828459045 3.141592653589793 1.414213562373095 1 1 2.718281828459045 1 -3 -2 24.70529422006547  ## Free Pascal See Delphi ## Frink All of the following operations work for any numerical type, including rational numbers, complex numbers and intervals of real numbers. e pi, π // Unicode can also be written in ASCII programs as \u03C0 sqrt[x] ln[x] // Natural log log[x] // Log to base 10 exp[x], e^x abs[x] floor[x] // Except for complex numbers where there's no good interpretation. ceil[x] // Except for complex numbers where there's no good interpretation. x^y ## FutureBasic window 1 text ,,,,, 60// set tab width print @"exp:", exp(1) print @"pi:", pi print @"sqr:", sqr(2) print @"log:", log(2) print @"log2:", log2(2) print @"log10", log10(2) print @"abs:", abs(-2) print @"floor:", int(1.534) print @"ceil:", val( using"###"; 1.534 ) print @"power:", 1.23 ^ 4 HandleEvents Output: exp: 2.7182818285 pi: 3.1415926536 sqr: 1.4142135624 log: 0.6931471806 log2: 1 log10 0.3010299957 abs: 2 floor: 2 ceil: 2 power: 2.28886641  ## Go package main import ( "fmt" "math" "math/big" ) func main() { // e and pi defined as constants. // In Go, that means they are not of a specific data type and can be used // as float32 or float64. Println takes the float64 values. fmt.Println("float64 values:") fmt.Println("e:", math.E) fmt.Println("π:", math.Pi) // The following functions all take and return the float64 data type. // square root. cube root also available (math.Cbrt) fmt.Println("square root(1.44):", math.Sqrt(1.44)) // natural logarithm--log base 10, 2 also available (math.Log10, math.Log2) // also available is log1p, the log of 1+x. (using log1p can be more // accurate when x is near zero.) fmt.Println("ln(e):", math.Log(math.E)) // exponential. also available are exp base 10, 2 (math.Pow10, math.Exp2) fmt.Println("exponential(1):", math.Exp(1)) fmt.Println("absolute value(-1.2):", math.Abs(-1.2)) fmt.Println("floor(-1.2):", math.Floor(-1.2)) fmt.Println("ceiling(-1.2):", math.Ceil(-1.2)) fmt.Println("power(1.44, .5):", math.Pow(1.44, .5)) // Equivalent functions for the float32 type are not in the standard // library. Here are the constants e and π as float32s however. fmt.Println("\nfloat32 values:") fmt.Println("e:", float32(math.E)) fmt.Println("π:", float32(math.Pi)) // The standard library has an arbitrary precision floating point type but // provides only the most basic methods. Also while the constants math.E // and math.Pi are provided to over 80 decimal places, there is no // convenient way of loading these numbers (with their full precision) // into a big.Float. A hack is cutting and pasting into a string, but // of course if you're going to do that you are free to cut and paste from // any other source. (The documentation cites OEIS as its source.) pi := "3.141592653589793238462643383279502884197169399375105820974944" π, _, _ := big.ParseFloat(pi, 10, 200, 0) fmt.Println("\nbig.Float values:") fmt.Println("π:", π) // Of functions requested by the task, only absolute value is provided. x := new(big.Float).Neg(π) y := new(big.Float) fmt.Println("x:", x) fmt.Println("abs(x):", y.Abs(x)) }  Output: float64 values: e: 2.718281828459045 π: 3.141592653589793 square root(1.44): 1.2 ln(e): 1 exponential(1): 2.718281828459045 absolute value(-1.2): 1.2 floor(-1.2): -2 ceiling(-1.2): -1 power(1.44, .5): 1.2 float32 values: e: 2.7182817 π: 3.1415927 big.Float values: π: 3.141592653589793238462643383279502884197169399375105820974944 x: -3.141592653589793238462643383279502884197169399375105820974944 abs(x): 3.141592653589793238462643383279502884197169399375105820974944  ## Groovy Math constants and functions are as outlined in the Java example, except as follows: Absolute Value In addition to the java.lang.Math.abs() method, each numeric type has an abs() method, which can be invoked directly on the number: println ((-22).abs())  Output: 22 Power In addition to the java.lang.Math.pow() method, each numeric type works with the power operator (**), which can be invoked as an in-fix operator between two numbers: println 22**3.5  Output: 49943.547010599876 Power results are not defined for all possible pairs of operands. Any power operation that does not have a result returns a 64-bit IEEE NaN (Not a Number) value. println ((-22)**3.5)  Output: NaN Also note that at the moment (07:00, 19 March 2011 (UTC)) Groovy (1.7.7) gives a mathematically incorrect result for "0**0". The correct result should be "NaN", but the Groovy operation result is "1". ## Haskell The operations are defined for the various numeric typeclasses, as defined in their type signature. exp 1 -- Euler number pi -- pi sqrt x -- square root log x -- natural logarithm exp x -- exponential abs x -- absolute value floor x -- floor ceiling x -- ceiling x ** y -- power (e.g. floating-point exponentiation) x ^ y -- power (e.g. integer exponentiation, nonnegative y only) x ^^ y -- power (e.g. integer exponentiation of rationals, also negative y)  ## HicEst Except for x^y, this is identical to Fortran: e ! Not available. Can be calculated EXP(1) pi ! Not available. Can be calculated 4.0*ATAN(1.0) x^0.5 ! square root LOG(x) ! natural logarithm LOG(x, 10) ! logarithm to base 10 EXP(x) ! exponential ABS(x) ! absolute value FLOOR(x) ! floor CEILING(x) ! ceiling x**y ! x raised to the y power x^y ! same as x**y ## Icon and Unicon link numbers # for floor and ceil procedure main() write("e=",&e) write("pi=",&pi) write("phi=",&phi) write("sqrt(2)=",sqrt(2.0)) write("log(e)=",log(&e)) write("log(100.,10)=",log(100,10)) write("exp(1)=",exp(1.0)) write("abs(-2)=",abs(-2)) write("floor(-2.2)=",floor(-2.2)) write("ceil(-2.2)=",ceil(-2.2)) write("power: 3^3=",3^3) end  Output: e=2.718281828459045 pi=3.141592653589793 phi=1.618033988749895 sqrt(2)=1.414213562373095 log(e)=1.0 log(100.,10)=2.0 exp(1)=2.718281828459045 abs(-2)=2 floor(-2.2)=-2 ceil(-2.2)=-3 ## J The examples below require arguments (x and y) to be numeric nouns. e =. 1x1 NB. Euler's number, specified as a numeric literal. e =. ^ 1 NB. Euler's number, computed by exponentiation. pi=. 1p1 NB. pi, specified as a numeric literal. pi=. o.1 NB. pi, computed trigonometrically. magnitude_of_x =. |x floor_of_x =. <.x ceiling_of_x =. >.x natural_log_of_x =. ^.x base_x_log_of_y =. x^.y x_squared =. *:x NB. special form x_squared =. x^2 NB. exponential form square_root_of_x =. %:x NB. special form square_root_of_x =. x^0.5 NB. exponential form x_to_the_y_power =. x^y  ## Java All of these functions are in Java's Math class which, does not require any imports: Math.E; //e Math.PI; //pi Math.sqrt(x); //square root--cube root also available (cbrt) Math.log(x); //natural logarithm--log base 10 also available (log10) Math.exp(x); //exponential Math.abs(x); //absolute value Math.floor(x); //floor Math.ceil(x); //ceiling Math.pow(x,y); //power  ## JavaScript Math.E Math.PI Math.sqrt(x) Math.log(x) Math.exp(x) Math.abs(x) Math.floor(x) Math.ceil(x) Math.pow(x,y)  ## jq The mathematical functions available in jq are defined as 0-arity filters, so to evaluate the sqrt of 4, one writes 4|sqrt. In jq, "." refers to the output coming from the left in the pipeline. In the following, comments appear after the "#": 1 | exp # i.e. e 1 | atan * 4 # i.e. π sqrt log # Naperian log exp length # absolute value if the argument is numeric floor ceil # requires jq >= 1.5 pow(x; y) # requires jq >= 1.5 ## Jsish /* real constants and functions, in JSI */ var x, y; ;Math.E; ;Math.PI; ;x = 100.0; ;Math.sqrt(x); ;Math.log(x); ;x = 2.0; ;Math.exp(x); ;x = -x; ;Math.abs(x); ;x = 42.42; ;Math.floor(x); ;Math.ceil(x); ;x = 10.0; ;y = 5; ;Math.pow(x,y); /* =!EXPECTSTART!= Math.E ==> 2.718281828459045 Math.PI ==> 3.141592653589793 x = 100.0 ==> 100 Math.sqrt(x) ==> 10 Math.log(x) ==> 4.605170185988092 x = 2.0 ==> 2 Math.exp(x) ==> 7.38905609893065 x = -x ==> -2 Math.abs(x) ==> 2 x = 42.42 ==> 42.42 Math.floor(x) ==> 42 Math.ceil(x) ==> 43 x = 10.0 ==> 10 y = 5 ==> 5 Math.pow(x,y) ==> 100000 =!EXPECTEND!= */  Output: prompt$ jsish --U real-constants.jsi
Math.E ==> 2.718281828459045
Math.PI ==> 3.141592653589793
x = 100.0 ==> 100
Math.sqrt(x) ==> 10
Math.log(x) ==> 4.605170185988092
x = 2.0 ==> 2
Math.exp(x) ==> 7.38905609893065
x = -x ==> -2
Math.abs(x) ==> 2
x = 42.42 ==> 42.42
Math.floor(x) ==> 42
Math.ceil(x) ==> 43
x = 10.0 ==> 10
y = 5 ==> 5
Math.pow(x,y) ==> 100000

# Run the unit tests
prompt$jsish -u real-constants.jsi [PASS] real-constants.jsi ## Julia e π, pi sqrt(x) log(x) exp(x) abs(x) floor(x) ceil(x) x^y  Note that Julia supports Unicode identifiers, and allows either π or pi for that constant. Also, mathematical constants like e and π in Julia are of a special type that is automatically converted to the correct precision when used in aritmetic operations. So, for example, BigFloat(2) * π computes 2π in arbitrary precision arithmetic. ## Kotlin All math constants are in kotlin.math. import kotlin.math.* fun main() { println(E) println(PI) println(sqrt(2.0)) println(ln(E)) println(log10(10.0)) println(log(4.0, 2.0)) // log base 2 of 4 println(exp(1.0)) println(abs(-1)) println(floor(-2.5)) println(ceil(-2.5)) println(2.5.pow(3.5)) // 2.5^3.5 }  Output: 2.718281828459045 3.141592653589793 1.4142135623730951 1.0 1.0 2.0 2.718281828459045 1 -3.0 -2.0 24.705294220065465  ## Lambdatalk {E} -> 2.718281828459045 {PI} -> 3.141592653589793 {sqrt 2} -> 1.4142135623730951 {log {E}} -> 1 {exp 1} -> 2.718281828459045 {abs -1} -> 1 {floor -2.5} -> -3 {ceil -2.5} -> -2 {pow 2.5 3.5} -> 24.705294220065465  ## Lasso //e define e => 2.7182818284590452 //π define pi => 3.141592653589793 e pi 9.0->sqrt 1.64->log 1.64->log10 1.64->exp 1.64->abs 1.64->floor 1.64->ceil 1.64->pow(10.0)  ## Liberty BASIC Ceiling and floor easily implemented as functions. sqr( is the LB function for square root. e & pi not available- calculate as shown. print exp( 1) ' e not available print 4 *atn( 1) ' pi not available x =12.345: y =1.23 print sqr( x), x^0.5 ' square root- NB the unusual name print log( x) ' natural logarithm base e print log( x) /2.303 ' base 10 logarithm print log( x) /log( y) ' arbitrary base logarithm print exp( x) ' exponential print abs( x) ' absolute value print floor( x) ' floor print ceiling( x) ' ceiling print x^y ' power end function floor( x) if x >0 then floor =int( x) else if x <>int( x) then floor =int( x) -1 else floor =int( x) end if end function function ceiling( x) if x <0 then ceiling =int( x) else ceiling =int( x) +1 end if end function ## Lingo the floatPrecision = 8 -- e (base of the natural logarithm) put exp(1) -- 2.71828183 -- pi put PI -- 3.14159265 -- square root put sqrt(2.0) -- 1.41421356 -- logarithm (any base allowed) x = 100 put log(x) -- calculate log for base e -- 4.60517019 put log(x)/log(10) -- calculate log for base 10 -- 2.00000000 -- exponential (ex) put exp(3) -- 20.08553692 -- absolute value (a.k.a. "magnitude") put abs(-1) -- 1 -- floor (largest integer less than or equal to this number--not the same as truncate or int) n = 23.536 put bitOr(n, 0) -- calculates floor -- 23 -- ceiling (smallest integer not less than this number--not the same as round up) n = 23.536 -- calculates ceil floor = bitOr(n, 0) if (floor >= n) then put floor else put floor+1 -- 24 -- power put power(2, 8) -- 256.00000000 ## LiveCode LC 7.1+, prior to this floor & ceil were not built-in. e‬: exp(1) pi: pi square root: sqrt(x) logarithm: log(x) exponential (‪ex‬): exp(x) absolute value: abs(x) floor: floor(x) ceiling: ceil(x) power: x^y ## Logo Works with: UCB Logo make "e exp 1 make "pi 2*(RADARCTAN 0 1) sqrt :x ln :x exp :x ; there is no standard abs, floor, or ceiling; only INT and ROUND. power :x :y ## Logtalk :- object(constants_and_functions). :- public(show/0). show :- write('e = '), E is e, write(E), nl, write('pi = '), PI is pi, write(PI), nl, write('sqrt(2) = '), SQRT is sqrt(2), write(SQRT), nl, % only base e logorithm is avaialable as a standard built-in function write('log(2) = '), LOG is log(2), write(LOG), nl, write('exp(2) = '), EXP is exp(2), write(EXP), nl, write('abs(-1) = '), ABS is abs(-1), write(ABS), nl, write('floor(-3.4) = '), FLOOR is floor(-3.4), write(FLOOR), nl, write('ceiling(-3.4) = '), CEILING is ceiling(-3.4), write(CEILING), nl, write('2 ** -3.4 = '), POWER is 2 ** -3.4, write(POWER), nl. :- end_object.  Output: | ?- constants_and_functions::show. e = 2.718281828459045 pi = 3.141592653589793 sqrt(2) = 1.4142135623730951 log(2) = 0.6931471805599453 exp(2) = 7.38905609893065 abs(-1) = 1 floor(-3.4) = -4 ceiling(-3.4) = -3 2 ** -3.4 = 0.09473228540689989 yes  ## Lua math.exp(1) math.pi math.sqrt(x) math.log(x) math.log10(x) math.exp(x) math.abs(x) math.floor(x) math.ceil(x) x^y  ## M2000 Interpreter Module Checkit { Def exp(x)= 2.71828182845905^x Print Ln(exp(1))==1 Print Log(10^5)==5 Print Sgn(-5)=-1 Print Abs(-2.10#)=2.1# Def exptype$(x)=type$(x) Print exptype$(Abs(-2.1#))="Currency"
Print exptype$(Abs(-2.1~))="Single" Print exptype$(Abs(-2.1@))="Decimal"
Print exptype$(Abs(-2&))="Long" Print exptype$(Abs(-2%))="Integer"
Print exptype$(Abs(-2.212e34))="Double" Print exptype$(Sgn(-2.1#))="Integer"
\\ Sgn return integer type
Print exptype$(Sgn(-2.212e34))="Integer" \\ Log, Len return double Print exptype$(Log(1000))="Double"
Print exptype$(exp(1%))="Double" Print exptype$(Ln(1212%))="Double"
\\ power return type Double ^ and ** (are the same)
Print exptype$(2&^2&)="Long" ' for Version <=11 is "Double" Print exptype$(2&**2&)="Long"  ' for Version <=11 is "Double"
Print exptype$(2&*2&)="Long" \\ 64bit Long Long (from Version 12) Print exptype$(2&&^2&&)="Long Long"
Print exptype$(2&&**2&&)="Long Long" Print exptype$(2&&*2&)="Long Long"
Print 2**2=4, 2^2=4, 2^2^2=16, 2**2**2=16
\\ floor() and Int() is the same
Print Int(-2.7)=-3, Int(2.7)=2
Print Floor(-2.7)=-3, Floor(2.7)=2
Print Ceil(-2.7)=-2, Ceil(2.7)=3

Print round(-2.7, 0)=-3, round(2.7, 0)=3
Print round(-2.2, 0)=-2, round(2.2, 0)=2

Print Sqrt(4)=2
}
Checkit

## Maple

> abs(ceil(floor(ln(exp(1)^sqrt(exp(Pi*I)+1)))));
0

## Mathematica/Wolfram Language

E
Pi
Sqrt[x]
Log[x]
Log[b,x]
Exp[x]
Abs[x]
Floor[x]
Ceiling[x]
Power[x, y]


Where x is the number, and b the base. Exp[x] can also be inputted as E^x or Ex and Power[x,y] can be also inputted as x^y or xy. All functions work with symbols, integers, floats and can be complex. Abs giving the modulus (|x|) if the argument is a complex number. Constant like E and Pi are kep unevaluated until someone explicitly tells it to give a numerical approximation: N[Pi,n] gives Pi to n-digit precision. Functions given an exact argument will be kept unevaluated if the answer can't be written more compact, approximate arguments will always be evaluated:

Log[1.23] => 0.207014
Log[10] => Log[10]
Log[10,100] => 2
Log[E^4] => 4
Log[1 + I] => Log[1+I]
Log[1. + I] => 0.346574 + 0.785398 I
Ceiling[Pi] => 4
Floor[Pi] => 3
Sqrt[2] => Sqrt[2]
Sqrt[4] => 2
Sqrt[9/2] => 3/Sqrt[2]
Sqrt[3.5] => 1.87083
Sqrt[-5 + 12 I] => 2 + 3 I
Sqrt[-4] => 2I
Exp[2] => E^2
Exp[Log[4]] => 4


## MATLAB / Octave

exp(1)    % e
pi        % pi
sqrt(x)   % square root
log(x)    % natural logarithm
log2(x)   % logarithm base 2
log10(x)  % logarithm base 10
exp(x)    % exponential
abs(-x)   % absolute value
floor(x)  % floor
ceil(x)   % ceiling
x^y       % power


## MAXScript

e       -- Euler's number
pi      -- pi
log x   -- natural logarithm
log10 x -- log base 10
exp x   -- exponantial
abs x   -- absolute value
floor x -- floor
ceil x  -- ceiling
pow x y -- power

## Mercury

math.pi         % Pi.
math.e          % Euler's number.
math.sqrt(X)    % Square root of X.
math.ln(X)      % Natural logarithm of X.
math.log10(X)   % Logarithm to the base 10 of X.
math.log2(X)    % Logarithm to the base 2 of X.
math.log(B, X)  % Logarithm to the base B of X.
math.exp(X)     % e raised to the power of X.
float.abs(X)    % Absolute value of X.
math.floor(X)   % Floor of X.
math.ceiling(X) % Ceiling of X.
math.pow(X, Y)  % X raised to the power of Y.


## Metafont

show mexp(256);   % outputs e; since MF uses mexp(x) = exp(x/256)
show 3.14159;     % no pi constant built in; of course we can define it
% in several ways... even computing
% C/2r (which would be funny since MF handles paths,
% and a circle is a path...)
show sqrt2;       % 1.41422, or in general sqrt(a)
show mexp(256*x); % see e.
show abs(x);      % returns |x| (the absolute value of the number x, or
% the length of the vector x); it is the same as
% length(x); plain Metafont in fact says:
% let abs = length;
show floor(x);    % floor
show ceiling(x);  % ceiling
show x**y;        % ** is not a built in: it is defined in the basic macros
% set for Metafont (plain Metafont) as a primarydef

## min

Works with: min version 0.19.3
e       ; e
pi      ; π
sqrt    ; square root
log10   ; common logarithm
log2    ; binary logarithm
; no exponential
; no absolute value
floor   ; greatest whole number smaller than or equal
ceil    ; smallest whole number greater than or equal
trunc   ; remove the fractional part (i.e. round towards 0)
round   ; round number to nth decimal place
pow     ; power

## МК-61/52

1	e^x	С/П

пи	С/П

КвКор	С/П

lg	С/П

e^x	С/П

|x|	С/П

П0	^	[x]	П1	-	x=0	09	ИП0	С/П	ЗН
x>=0	14	ИП1	С/П	ИП1	1	-	С/П

П0	^	[x]	П1	-	x=0	09	ИП0	С/П	ЗН
x<0	14	ИП1	С/П	ИП1	1	+	С/П

x^y	С/П


## Modula-3

Modula-3 uses a module that is a wrapper around C's math.h.

Note that all of these procedures (except the built ins) take LONGREALs as their argument, and return LONGREALs.

Math.E;
Math.Pi;
Math.sqrt(x);
Math.log(x);
Math.exp(x);
ABS(x); (* Built in function. *)
FLOOR(x); (* Built in function. *)
CEILING(x); (* Built in function. *)
Math.pow(x, y);


## Neko

/**
Real constants and functions, in Neko
Tectonics:
nekoc real-constants.neko
neko real-constants
*/

var euler = $loader.loadprim("std@math_exp", 1)(1) var pi =$loader.loadprim("std@math_pi", 0)()

var math_sqrt = $loader.loadprim("std@math_sqrt", 1) var math_log =$loader.loadprim("std@math_log", 1)
var math_exp = $loader.loadprim("std@math_exp", 1) var math_abs =$loader.loadprim("std@math_abs", 1)
var math_floor = $loader.loadprim("std@math_floor", 1) var math_ceil =$loader.loadprim("std@math_ceil", 1)
var math_pow = $loader.loadprim("std@math_pow", 2)$print("Euler      : ", euler, "\n")
$print("Pi : ", pi, "\n")$print("Sqrt(2)    : ", math_sqrt(2), "\n")
$print("Log(10) : ", math_log(10), "\n")$print("Exp(1)     : ", math_pow(euler, 1), "\n")
$print("Abs(-2.2) : ", math_abs(-2.2), "\n")$print("Floor(-2.2): ", math_floor(-2.2), "\n")
$print("Ceil(-2.2) : ", math_ceil(-2.2), "\n")$print("Pow(2, 8)  : ", math_pow(2, 8), "\n")

Output:
prompt$nekoc real-contstants.neko prompt$ neko real-contstants.n
Euler      : 2.71828182845905
Pi         : 3.14159265358979
Sqrt(2)    : 1.4142135623731
Log(10)    : 2.30258509299405
Exp(1)     : 2.71828182845905
Abs(-2.2)  : 2.2
Floor(-2.2): -3
Ceil(-2.2) : -2
Pow(2, 8)  : 256

## NetRexx

All the required constants and functions (and more) are in Java's Math class. NetRexx also provides a limited set of built in numeric manipulation functions for it's Rexx object.

/* NetRexx */
options replace format comments java crossref symbols nobinary utf8

numeric digits 30

x = 2.5
y = 3
say
say 'Java Math constants & functions:'
say Rexx('  Euler''s number (e):').left(pad)                    Math.E
say Rexx('  Square root of' x':').left(pad)                     Math.sqrt(x)
say Rexx('  Log(e) of' x':').left(pad)                          Math.log(x)
say Rexx('  Log(e) of e:').left(pad)                            Math.log(Math.E)
say Rexx('  Log(10) of' x':').left(pad)                         Math.log10(x)
say Rexx('  Log(10) of 10:').left(pad)                          Math.log10(10)
say Rexx('  Exponential (e**x) of' x':').left(pad)              Math.exp(x)
say Rexx('  Exponential (e**x) of log(e)' x':').left(pad)       Math.exp(Math.log(x))
say Rexx('  Abs of' x':').left(pad)                             Math.abs(x.todouble)
say Rexx('  Abs of' (-x)':').left(pad)                          Math.abs((-x).todouble)
say Rexx('  Floor of' x':').left(pad)                           Math.floor(x)
say Rexx('  Floor of' (-x)':').left(pad)                        Math.floor((-x))
say Rexx('  Ceiling of' x':').left(pad)                         Math.ceil(x)
say Rexx('  Ceiling of' (-x)':').left(pad)                      Math.ceil((-x))
say Rexx(' ' x 'to the power of' y':').left(pad)                Math.pow(x, y)
say Rexx(' ' x 'to the power of' 1 / y':').left(pad)            Math.pow(x, 1 / y)
say Rexx('  10 to the power of log10' x':').left(pad)           Math.pow(10, Math.log10(x))

-- Extras
say Rexx('  Cube root of' x':').left(pad)                       Math.cbrt(x)
say Rexx('  Hypotenuse of' 3 'x' 4 'right triangle:').left(pad) Math.hypot(3, 4)
say Rexx('  Max of' (-x) '&' x':').left(pad)                    Math.max((-x).todouble, x)
say Rexx('  Min of' (-x) '&' x':').left(pad)                    Math.min((-x).todouble, x)
say Rexx('  Signum of' x':').left(pad)                          Math.signum((x).todouble)
say Rexx('  Signum of' x '-' x':').left(pad)                    Math.signum((x - x).todouble)
say Rexx('  Signum of' (-x)':').left(pad)                       Math.signum((-x).todouble)

say
say 'NetRexx built-in support for numeric data:'
say Rexx('  Abs of' x':').left(pad)                        x.abs()
say Rexx('  Abs of' (-x)':').left(pad)                     (-x).abs()
say Rexx('  Sign of' x':').left(pad)                       x.sign()
say Rexx('  Sign of' x '-' x':').left(pad)                 (x - x).sign()
say Rexx('  Sign of' (-x)':').left(pad)                    (-x).sign()
say Rexx('  Max of' (-x) '&' x':').left(pad)               (-x).max(x)
say Rexx('  Min of' (-x) '&' x':').left(pad)               (-x).min(x)
say Rexx('  Truncate' x 'by' y':').left(pad)               x.trunc(y)
say Rexx('  Format (with rounding)' x 'by' y':').left(pad) x.format(y, 0)

Output:
Java Math constants & functions:
Euler's number (e):                    2.718281828459045
Pi:                                    3.141592653589793
Square root of 2.5:                    1.58113883008419
Log(e) of 2.5:                         0.9162907318741551
Log(e) of e:                           1
Log(10) of 2.5:                        0.3979400086720376
Log(10) of 10:                         1
Exponential (e**x) of 2.5:             12.18249396070347
Exponential (e**x) of log(e) 2.5:      2.5
Abs of 2.5:                            2.5
Abs of -2.5:                           2.5
Floor of 2.5:                          2
Floor of -2.5:                         -3
Ceiling of 2.5:                        3
Ceiling of -2.5:                       -2
2.5 to the power of 3:                 15.625
2.5 to the power of 0.3333333333333333 1.357208808297453
10 to the power of log10 2.5:          2.5
Cube root of 2.5:                      1.357208808297453
Hypotenuse of 3 x 4 right triangle:    5
Max of -2.5 & 2.5:                     2.5
Min of -2.5 & 2.5:                     -2.5
Signum of 2.5:                         1
Signum of 2.5 - 2.5:                   0
Signum of -2.5:                        -1

NetRexx built-in support for numeric data:
Abs of 2.5:                            2.5
Abs of -2.5:                           2.5
Sign of 2.5:                           1
Sign of 2.5 - 2.5:                     0
Sign of -2.5:                          -1
Max of -2.5 & 2.5:                     2.5
Min of -2.5 & 2.5:                     -2.5
Truncate 2.5 by 3:                     2.500
Format (with rounding) 2.5 by 3:         3


## Nim

import math

var x, y = 12.5

echo E
echo PI
echo sqrt(x)
echo ln(x)
echo log10(x)
echo exp(x)
echo abs(x)
echo floor(x)
echo ceil(x)
echo pow(x, y)


## Objeck

Float->Pi();
Float->E();
4.0->SquareRoot();
1.5->Log();
# exponential is not supported
3.99->Abs();
3.99->Floor();
3.99->Ceiling();
4.5->Ceiling(2.0);

## OCaml

Unless otherwise noted, the following functions are for floats only:

Float.pi    (* pi *)
sqrt x      (* square root *)
log x       (* natural logarithm--log base 10 also available (log10) *)
exp x       (* exponential *)
abs_float x (* absolute value *)
abs x       (* absolute value (for integers) *)
floor x     (* floor *)
ceil x      (* ceiling *)
x ** y      (* power *)
-. x        (* negation for floats *)


## Octave

e         % e
pi        % pi
sqrt(pi)  % square root
log(e)    % natural logarithm
exp(pi)   % exponential
abs(-e)   % absolute value
floor(pi) % floor
ceil(pi)  % ceiling
e**pi     % power


## Oforth

import: math

: testReal
E println
Pi println
9 sqrt println
2 ln println
2 exp println
-3.4 abs println
3.4 exp println

2.4 floor println
3.9 floor println
5.5 floor println
-2.4 floor println
-3.9 floor println
-5.5 floor println

2.4 ceil println
3.9 ceil println
5.5 ceil println
-2.4 ceil println
-3.9 ceil println
-5.5 ceil println ;

## ooRexx

Translation of: NetRexx
Uses: RxMath
/* Rexx */

-- MathLoadFuncs & MathDropFuncs are no longer needed and are effectively NOPs
-- but MathLoadFuncs does return its copyright statement when given a string argument

numeric digits 16

x = 2.5
y = 3
digs = digits()
say
say 'Working with precision' digs
say 'Math constants & functions:'
say ('  Euler''s number (e):')~left(pad)                    RxCalcExp(1, digs)
say ('  Square root of' x':')~left(pad)                     RxCalcSqrt(x, digs)
say ('  Log(e) of' x':')~left(pad)                          RxCalcLog(x, digs)
say ('  Log(e) of e:')~left(pad)                            RxCalcLog(RxCalcExp(1, digs), digs)
say ('  Log(10) of' x':')~left(pad)                         RxCalcLog10(x, digs)
say ('  Log(10) of 10:')~left(pad)                          RxCalcLog10(10, digs)
say ('  Exponential (e**x) of' x':')~left(pad)              RxCalcExp(x, digs)
say ('  Exponential (e**x) of log(e)' x':')~left(pad)       RxCalcExp(RxCalcLog(x, digs), digs)
say (' ' x 'to the power of' y':')~left(pad)                RxCalcPower(x, y, digs)
say (' ' x 'to the power of 1/'y':')~left(pad)              RxCalcPower(x, 1 / y, digs)
say ('  10 to the power of log10' x':')~left(pad)           RxCalcPower(10, RxCalcLog10(x), digs)

say
say 'Rexx built-in support for numeric data:'
say ('  Abs of' x':')~left(pad)                             x~abs()
say ('  Abs of' (-x)':')~left(pad)                          (-x)~abs()
say ('  Sign of' x':')~left(pad)                            x~sign()
say ('  Sign of' x '-' x':')~left(pad)                      (x - x)~sign()
say ('  Sign of' (-x)':')~left(pad)                         (-x)~sign()
say ('  Max of' (-x) '&' x':')~left(pad)                    (-x)~max(x)
say ('  Min of' (-x) '&' x':')~left(pad)                    (-x)~min(x)
say ('  Truncate' x 'by' y':')~left(pad)                    x~trunc(y)
say ('  Format (with rounding)' x 'by' y':')~left(pad)      x~format(y, 0)

say
say 'Use RYO functions for floor & ceiling:'
say ('  Floor of' x':')~left(pad)                           floor(x)
say ('  Floor of' (-x)':')~left(pad)                        floor((-x))
say ('  Ceiling of' x':')~left(pad)                         ceiling(x)
say ('  Ceiling of' (-x)':')~left(pad)                      ceiling((-x))

return

-- floor and ceiling functions are not part of ooRexx
floor: procedure
return arg(1)~trunc() - (arg(1) < 0) * (arg(1) \= arg(1)~trunc())

ceiling: procedure
return arg(1)~trunc() + (arg(1) > 0) * (arg(1) \= arg(1)~trunc())

::requires 'RxMath' library

Output:
rxmath 1.1 - REXX mathematical function package

Working with precision 16
Math constants & functions:
Euler's number (e):                    2.718281828459045
Pi:                                    3.141592653589793
Square root of 2.5:                    1.581138830084190
Log(e) of 2.5:                         0.9162907318741551
Log(e) of e:                           1
Log(10) of 2.5:                        0.3979400086720376
Log(10) of 10:                         1
Exponential (e**x) of 2.5:             12.18249396070347
Exponential (e**x) of log(e) 2.5:      2.5
2.5 to the power of 3:                 15.625
2.5 to the power of 1/3:               1.357208808297453
10 to the power of log10 2.5:          2.5

Rexx built-in support for numeric data:
Abs of 2.5:                            2.5
Abs of -2.5:                           2.5
Sign of 2.5:                           1
Sign of 2.5 - 2.5:                     0
Sign of -2.5:                          -1
Max of -2.5 & 2.5:                     2.5
Min of -2.5 & 2.5:                     -2.5
Truncate 2.5 by 3:                     2.500
Format (with rounding) 2.5 by 3:         3

Use RYO functions for floor & ceiling:
Floor of 2.5:                          2
Floor of -2.5:                         -3
Ceiling of 2.5:                        3
Ceiling of -2.5:                       -2


## Oz

{ForAll
[
{Exp 1.}           %% 2.7183   Euler's number: not predefined
4. * {Atan2 1. 1.} %% 3.1416   pi: not predefined
{Sqrt 81.}         %% 9.0      square root; expects a float
{Log 2.7183}       %% 1.0      natural logarithm
{Abs ~1}           %% 1        absolute value; expects a float or an integer
{Floor 1.999}      %% 1.0      floor; expects and returns a float
{Ceil 1.999}       %% 2.0      ceiling; expects and returns a float
{Pow 2 3}          %% 8        power; both arguments must be of the same type
]
Show}

## PARI/GP

[exp(1), Pi, sqrt(2), log(2), abs(2), floor(2), ceil(2), 2^3]

## Pascal

Following functions are defined by ISO standard 7185, Standard “Unextended” Pascal, and supported by any processor:

	{ Euler’s constant }
exp(1)
{ principal square root of x }
sqrt(x)
{ natural logarithm }
ln(x)
{ exponential }
exp(x)
{ absolute value }
abs(x)

Works with: Extended Pascal

Additionally, in Extended Pascal (ISO standard 10206) following operators and expressions can be used:

	{ Pi }
2 * arg(cmplx(0.0, maxReal))
{ power, yields same data type as base, exponent has to be an integer }
base pow exponent
{ real power, exponent may be an integer or real value, yet base and }
{ exponent are automatically promoted to an approximate real value, result }
{ is complex if base is complex, otherwise a real value }
base ** exponent


Exp, sqrt, ln, and exp return real values, but a complex value if supplied with a complex value. Abs returns an integer value if supplied with an integer, otherwise a real value.

## Perl

use POSIX; # for floor() and ceil()

exp(1); # e
4 * atan2(1, 1); # pi
sqrt($x); # square root log($x); # natural logarithm; log10() available in POSIX module
exp($x); # exponential abs($x); # absolute value
floor($x); # floor ceil($x); # ceiling
$x **$y; # power

use Math::Trig;
pi; # alternate way to get pi

use Math::Complex;
pi; # alternate way to get pi


## Phix

?E                  -- Euler number
?PI                 -- pi
?log(E)             -- natural logarithm
?log10(10)          -- base 10 logarithm
?exp(log(5))        -- exponential
?sqrt(5)            -- square root
?abs(-1.2)          -- absolute value
?floor(-1.2)        -- floor,    -2
?ceil(-1.2)         -- ceiling,  -1
?round(-1.8)        -- rounded,  -2
?trunc(-1.8)        -- truncate, -1
?power(E,log(5))    -- displays 5.0
?power(10,log10(5)) -- displays 5.0
?INVLN10            -- displays 0.434..
?exp(1/INVLN10)     -- displays 10.0


## PHP

M_E; //e
M_PI; //pi
sqrt(x); //square root
log(x); //natural logarithm--log base 10 also available (log10)
exp(x); //exponential
abs(x); //absolute value
floor(x); //floor
ceil(x); //ceiling
pow(x,y); //power


## Picat

main =>
println(math.e),
println(math.pi),
nl,

println(sqrt(2)),
nl,

println(log(10)),                % base e
println(log(math.pi,10)),        % some base, here pi
println(log2(10)),               % base 2
println(exp(2.302585092994046)),
nl,

println(abs(- math.e)),
nl,
println(floor(sqrt(101))),
println(ceiling(sqrt(101))),
nl,
println(math.pi**math.e),        % power
println(pow(math.pi,math.e)),    % power
nl.
Output:
2.718281828459045
3.141592653589793

1.414213562373095

2.302585092994046
2.011465867588061
3.321928094887362
10.000000000000002

2.718281828459045

10
11

22.459157718361041
22.459157718361041

## PicoLisp

PicoLisp has only limited floating point support (scaled bignum arithmetics). It can handle real numbers with as many positions after the decimal point as desired, but is practically limited by the precision of the C-library functions (about 16 digits). The default precision is six, and can be changed with 'scl':

(scl 12)  # 12 places after decimal point

(prinl (format (exp 1.0) *Scl))        # e, exp
(prinl (format pi *Scl))               # pi

(prinl (format (pow 2.0 0.5) *Scl))    # sqare root
(prinl (format (sqrt 2.0 1.0) *Scl))

(prinl (format (log 2.0) *Scl))        # logarithm
(prinl (format (exp 4.0) *Scl))        # exponential

(prinl (format (abs -7.2) *Scl))       # absolute value
(prinl (abs -123))

(prinl (format (pow 3.0 4.0) *Scl))    # power
Output:
2.718281828459
3.141592653590
1.414213562373
1.414213562373
0.693147180560
54.598150033144
7.200000000000
123
81.000000000000

## PL/I

/* e  not available other than by using exp(1q0).*/
/* pi not available other than by using a trig function such as: pi=4*atan(1) */
y = sqrt(x);
y = log(x);
y = log2(x);
y = log10(x);
y = exp(x);
y = abs(x);
y = floor(x);
y = ceil(x);
a = x**y;      /* power */
/* extra functions: */
y = erf(x);    /* the error function. */
y = erfc(x);   /* the error function complemented. */
y = gamma (x);
y = loggamma (x);

## Pop11

pi        ;;; Number Pi
sqrt(x)   ;;; Square root
log(x)    ;;; Natural logarithm
exp(x)    ;;; Exponential function
abs(x)    ;;; Absolute value
x ** y    ;;; x to the power y

The number e is not provided directly, one has to compute 'exp(1)' instead. Also, f/math>)

## PowerShell

Since PowerShell has access to .NET all this can be achieved using the .NET Base Class Library:

Write-Host ([Math]::E)
Write-Host ([Math]::Pi)
Write-Host ([Math]::Sqrt(2))
Write-Host ([Math]::Log(2))
Write-Host ([Math]::Exp(2))
Write-Host ([Math]::Abs(-2))
Write-Host ([Math]::Floor(3.14))
Write-Host ([Math]::Ceiling(3.14))
Write-Host ([Math]::Pow(2, 3))


## PureBasic

Debug #E
Debug #PI
Debug Sqr(f)
Debug Log(f)
Debug Exp(f)
Debug Log10(f)
Debug Abs(f)
Debug Pow(f,f)


## Python

import math

math.e          # e
math.pi         # pi
math.sqrt(x)    # square root  (Also commonly seen as x ** 0.5 to obviate importing the math module)
math.log(x)     # natural logarithm
math.log10(x)   # base 10 logarithm
math.exp(x)     # e raised to the power of x
abs(x)          # absolute value
math.floor(x)   # floor
math.ceil(x)    # ceiling
x ** y          # exponentiation
pow(x, y[, n])  # exponentiation [, modulo n (useful in certain encryption/decryption algorithms)]

# The math module constants and functions can, of course, be imported directly by:
#   from math import e, pi, sqrt, log, log10, exp, floor, ceil


## R

exp(1)             # e
pi                 # pi
sqrt(x)            # square root
log(x)             # natural logarithm
log10(x)           # base 10 logarithm
log(x, y)          # arbitrary base logarithm
exp(x)             # exponential
abs(x)             # absolute value
floor(x)           # floor
ceiling(x)         # ceiling
x^y                # power


## Racket

(exp 1)         ; e
pi              ; pi
(sqrt x)        ; square root
(log x)         ; natural logarithm
(exp x)         ; exponential
(abs x)         ; absolute value
(floor x)       ; floor
(ceiling x)     ; ceiling
(expt x y)      ; power


## Raku

(formerly Perl 6)

say e;            # e
say π; # or pi    # pi
say τ; # or tau   # tau

# Common mathmatical function are availble
# as subroutines and as numeric methods.
# It is a matter of personal taste and
# programming style as to which is used.
say sqrt 2;       # Square root
say 2.sqrt;       # Square root

# If you omit a base, does natural logarithm
say log 2;        # Natural logarithm
say 2.log;        # Natural logarithm

# Specify a base if other than e
say log 4, 10;    # Base 10 logarithm
say 4.log(10);    # Base 10 logarithm
say 4.log10;      # Convenience, base 10 only logarithm

say exp 7;        # Exponentiation base e
say 7.exp;        # Exponentiation base e

# Specify a base if other than e
say exp 7, 4;     # Exponentiation
say 7.exp(4);     # Exponentiation
say 4 ** 7;       # Exponentiation

say abs -2;       # Absolute value
say (-2).abs;     # Absolute value

say floor -3.5;   # Floor
say (-3.5).floor; # Floor

say ceiling pi;   # Ceiling
say pi.ceiling;   # Ceiling

say e ** π\i + 1 ≅ 0; # :-)


## REXX

REXX has no built-in functions for trig functions, square root, pi, exponential (e raised to a power), logarithms and other similar functions.

REXX doesn't have any built-in (math) constants.

### abs

a=abs(y)                       /*takes the absolute value of y.*/


### exponentiation (**)

r=x**y                         /*REXX only supports integer powers.*/
/*Y may be negative, zero, positive.*/
/*X may be any real number.         */


### ceiling

A ceiling function for REXX:

ceiling: procedure; parse arg x; t=trunc(x); return t+(x>0)*(x\=t)


### floor

A floor function for REXX:

floor:   procedure; parse arg x; t=trunc(x); return t-(x<0)-(x\=t)


### sqrt (optimized)

A [principal] square root (SQRT) function for REXX   (with arbitrary precision):

/*──────────────────────────────────SQRT subroutine───────────────────────────*/
sqrt: procedure;  parse arg x;         if x=0  then return 0  /*handle 0 case.*/
if \datatype(x,'N')  then return '[n/a]'   /*Not Applicable ───if not numeric.*/
i=;  if x<0  then do; x=-x; i='i'; end /*handle complex numbers if  X  is < 0.*/
d=digits()                             /*get the current numeric precision.   */
m.=9                                   /*technique uses just enough digits.   */
h=d+6                                  /*use extra decimal digits for accuracy*/
numeric digits 9                       /*use "small" precision at first.      */
numeric form                           /*force scientific form of the number. */
if fuzz()\==0  then numeric fuzz 0     /*just in case invoker has a FUZZ  set.*/
parse value format(x,2,1,,0)  'E0'  with  g 'E' _ .  /*get the  X's  exponent.*/
g=(g * .5) || 'e' || (_ % 2)      /*1st guesstimate for the square root. */
/* g= g * .5     'e'    (_ % 2) */   /*a shorter & concise version of above.*/
/*Note: to insure enough accuracy for  */
/*  the result, the precision during   */
/*  the SQRT calculations is increased */
/*  by two extra decimal digits.       */
do j=0  while  h>9;  m.j=h;  h=h%2+1 /*compute the sizes (digs) of precision*/
end   /*j*/                          /* [↑]  precisions are stored in  M.   */
/*now, we start to do the heavy lifting*/
do k=j+5  to 0  by -1                /*compute the  √  with increasing digs.*/
numeric digits m.k                   /*each iteration, increase the digits. */
g=(g+x/g) * .5                       /*perform the nitty-gritty calculations*/
end   /*k*/                          /* [↑]  * .5   is faster than   / 2    */
/* [↓]  normalize √ ──► original digits*/
numeric digits d                       /* [↓]  make answer complex if  X < 0. */
return (g/1)i                          /*normalize, and add possible I suffix.*/

  ╔════════════════════════════════════════════════════════════════════╗
╔═╝                                __                                  ╚═╗
║                                 √                                      ║
║                                                                        ║
║ While the above REXX code seems like it's doing a lot of extra work,   ║
║ it saves a substantial amount of processing time when the precision    ║
║ (DIGITs)  is a lot greater than the default  (default is nine digits). ║
║                                                                        ║
║ Indeed, when computing square roots in the hundreds  (even thousands)  ║
║ of digits,  this technique reduces the amount of CPU processing time   ║
║ by keeping the length of the computations to a minimum (due to a large ║
║ precision),  while the accuracy at the beginning isn't important for   ║
║ calculating the (first) guesstimate  (the running square root guess).  ║
║                                                                        ║
║ Each iteration of   K   (approximately) doubles the number of digits,  ║
║ but takes almost four times longer to compute  (actually, around 3.8). ║
║                                                                        ║
║ The REXX code could be streamlined (pruned)  by removing  the          ║
║ The    NUMERIC FUZZ 0      statement can be removed  if  it is known   ║
║ that  it is already set to zero.  (which is the default).              ║
║                                                                        ║
║ Also, the   NUMERIC FORM   statement can be removed  if  it is known   ║
║ that the   form  is  SCIENTIFIC   (which is the default).              ║
║                                  __                                    ║
╚═╗                               √                                    ╔═╝
╚════════════════════════════════════════════════════════════════════╝


### sqrt (simple)

/*──────────────────────────────────SQRT subroutine─────────────────────*/
sqrt: procedure;  arg x                /*a simplistic  SQRT  subroutine.*/
if x=0  then return 0                  /*handle special case of zero.   */
d=digits()                             /*get the current precision (dig)*/
numeric digits d+2                     /*ensure extra precision (2 digs)*/
g=x/4                                  /*try get a so-so 1st guesstimate*/
old=0                                  /*set OLD guess to zero.         */
do forever           /*keep at it 'til  G (guess)=old.*/
g=(g+x/g) / 2        /*do the nitty-gritty calculation*/
if g=old  then leave /*if G is the same as old, quit. */
old=g                /*save OLD for next iteration.   */
end   /*forever*/    /* [↑] ···'til we run out of digs*/
numeric digits d                       /*restore the original precision.*/
return g/1                             /*normalize to old precision (d).*/


### other

Other mathematical-type functions supported are:

numeric digits ddd               /*sets the current precision to  DDD   */
numeric fuzz   fff               /*arithmetic comparisons with FFF fuzzy*/
numeric form   kkk               /*exponential: scientific | engineering*/

low=min(a,b,c,d,e,f,g, ...)      /*finds the min of specified arguments.*/
big=min(a,b,c,d,e,f,g, ...)      /*finds the max of specified arguments.*/

rrr=random(low,high)             /*gets a random integer from LOW-->HIGH*/
arr=random(low,high,seed)        /* ... with a seed (to make repeatable)*/

mzp=sign(x)                      /*finds the sign of  x   (-1, 0, +1).  */

fs=format(x)                    /*formats X  with the current DIGITS() */
fb=format(x,bbb)                /*            BBB  digs  before decimal*/
fa=format(x,bbb,aaa)            /*            AAA  digs  after  decimal*/
fa=format(x,,0)                 /*            rounds  X  to an integer.*/
fe=format(x,,eee)               /*            exponent has eee places. */
ft=format(x,,eee,ttt)           /*if x exceeds TTT digits, force exp.  */

hh=b2x(bbb)                      /*converts binary/bits to hexadecimal. */
dd=c2d(ccc)                      /*converts character   to decimal.     */
hh=c2x(ccc)                      /*converts character   to hexadecimal. */
cc=d2c(ddd)                      /*converts decimal     to character.   */
hh=d2x(ddd)                      /*converts decimal     to hexadecimal. */
bb=x2b(hhh)                      /*converts hexadecimal to binary (bits)*/
cc=x2c(hhh)                      /*converts hexadecimal to character.   */
dd=x2d(hhh)                      /*converts hexadecimal to decimal.     */


## Ring

See "Mathematical Functions" + nl
See "Sin(0) = " + sin(0) + nl
See "Sin(90) radians = " + sin(90) + nl
See "Sin(90) degree = " + sin(90*3.14/180) + nl

See "Cos(0) = " + cos(0) + nl
See "Cos(90) radians = " + cos(90) + nl
See "Cos(90) degree = " + cos(90*3.14/180) + nl

See "Tan(0) = " + tan(0) + nl
See "Tan(90) radians = " + tan(90) + nl
See "Tan(90) degree = " + tan(90*3.14/180) + nl

See "asin(0) = " + asin(0) + nl
See "acos(0) = " + acos(0) + nl
See "atan(0) = " + atan(0) + nl
See "atan2(1,1) = " + atan2(1,1) + nl

See "sinh(0) = " + sinh(0) + nl
See "sinh(1) = " + sinh(1) + nl
See "cosh(0) = " + cosh(0) + nl
See "cosh(1) = " + cosh(1) + nl
See "tanh(0) = " + tanh(0) + nl
See "tanh(1) = " + tanh(1) + nl

See "exp(0) = " + exp(0) + nl
See "exp(1) = " + exp(1) + nl
See "log(1) = " + log(1) + nl
See "log(2) = " + log(2) + nl
See "log10(1) = " + log10(1) + nl
See "log10(2) = " + log10(2) + nl
See "log10(10) = " + log10(10) + nl

See "Ceil(1.12) = " + Ceil(1.12) + nl
See "Ceil(1.72) = " + Ceil(1.72) + nl

See "Floor(1.12) = " + floor(1.12) + nl
See "Floor(1.72) = " + floor(1.72) + nl

See "fabs(1.12) = " + fabs(1.12) + nl
See "fabs(1.72) = " + fabs(1.72) + nl

See "pow(2,3) = " + pow(2,3) + nl

see "sqrt(16) = " + sqrt(16) + nl

## RLaB

### Mathematical Constants

RLaB has a number of mathematical constants built-in within the list const. These facilities are provided through the Gnu Science Library [[1]].

>> const
e                    euler           ln10            ln2             lnpi
log10e               log2e           pi              pihalf          piquarter
rpi                  sqrt2           sqrt2r          sqrt3           sqrtpi
tworpi

### Physical Constants

Another list of physical constants and unit conversion factors exists and is called mks. Here the conversion goes between that particular unit and the equivalent unit in, one and only, metric system.

>> mks
F                    G               J               L               N
Na                   R0              Ry              Tsp             V0
a                    a0              acre            alpha           atm
au                   bar             barn            btu             c
cal                  cgal            cm              cm2             cm3
ct                   cup             curie           day             dm
dm2                  dm3             dyne            e               eV
eps0                 erg             fathom          floz            ft
ftcan                ftlam           g               gal             gauss
gf                   h               ha              hbar            hour
hp                   in              inH2O           inHg            kSB
kb                   kcal            km              km2             km3
kmh                  knot            kpf             lam             lb
lumen                lux             ly              mHg             mSun
me                   micron          mil             mile            min
mm                   mm2             mm3             mmu             mn
mp                   mph             mu0             mub             mue
mun                  mup             nmi             oz              pal
parsec               pf              phot            poise           psi
therm                tntton          ton             torr            toz
tsp                  uam             ukgal           ukton           uston
week                 yd

### Elementary Functions

>> x = rand()
>> sqrt(x)
2.23606798
>> log(x)
1.60943791
>> log10(x)
0.698970004
>> exp(x)
148.413159
>> abs(x)
5
>> floor(x)
5
>> ceil(x)
5
>> x .^ 2
25

## Ruby

x.abs #absolute value
x.magnitude #absolute value
x.floor #floor
x.ceil #ceiling
x ** y #power
include Math
E #e
PI #pi
sqrt(x) #square root
log(x) #natural logarithm
log(x, y) #logarithm base y
log10(x) #base 10 logarithm
exp(x) #exponential


## Run BASIC

print "exp:";chr$(9); EXP(1) print "PI:";chr$(9);    22/7
print "Sqr2:";chr$(9); SQR(2) print "Log2:";chr$(9);  LOG(2) : REM Base 10
print "Exp2:";chr$(9); EXP(2) print "Abs2:";chr$(9);  ABS(-2)
print "Floor:";chr$(9); INT(1.534) print "ceil:";chr$(9);  val(using("###",1.534))
print "Power:";chr$(9); 1.23^4 exp: 2.71828183 PI: 3.14285707 Sqr2: 1.41421356 Log2: 0.693147181 Exp2: 7.3890561 Abs2: 2 Floor: 1 ceil: 2 Power: 2.28886641 ## Rust use std::f64::consts::*; fn main() { // e (base of the natural logarithm) let mut x = E; // π x += PI; // square root x = x.sqrt(); // logarithm (any base allowed) x = x.ln(); // ceiling (smallest integer not less than this number--not the same as round up) x = x.ceil(); // exponential (ex) x = x.exp(); // absolute value (a.k.a. "magnitude") x = x.abs(); // floor (largest integer less than or equal to this number--not the same as truncate or int) x = x.floor(); // power (xy) x = x.powf(x); assert_eq!(x, 4.0); }  ## Scala object RealConstantsFunctions extends App{ println(math.E) // e println(math.Pi) // pi println(math.sqrt(2.0)) // square root println(math.log(math.E)) // log to base e println(math.log10(10.0)) // log to base 10 println(math.exp(1.0)) // exponential println(math.abs(-1)) // absolute value println(math.floor(-2.5)) // floor println(math.ceil(-2.5)) // ceiling println(math.pow(2.5, 3.5)) // power }  ## Scheme (sqrt x) ;square root (log x) ;natural logarithm (exp x) ;exponential (abs x) ;absolute value (floor x) ;floor (ceiling x) ;ceiling (expt x y) ;power  ## Seed7 The math.s7i library defines:  E # e (Euler's number) PI # Pi sqrt(x) # square root log(x) # natural logarithm - log base 10 is also available: log10(x)) exp(x) # exponential abs(x) # absolute value floor(x) # floor ceil(x) # ceiling The float.s7i library defines:  x ** y # power with integer exponent x ** y # power with float exponent ## Sidef Num.e # e Num.pi # pi x.sqrt # square root x.log # natural logarithm x.log10 # base 10 logarithm x.exp # e raised to the power of x x.abs # absolute value x.floor # floor x.ceil # ceiling x**y # exponentiation  ## Slate numerics E. numerics Pi. n sqrt. n log10. "base 10 logarithm" n ln. "natural logarithm" n log: m. "arbitrary base logarithm" n exp. "exponential" n abs. "absolute value" n floor. n ceiling. n raisedTo: anotherNumber ## Smalltalk Float e. Float pi. aNumber sqrt. aNumber log. "base 10 logarithm" aNumber ln. "natural logarithm" aNumber exp. "exponential" aNumber abs. "absolute value" aNumber floor. aNumber ceiling. aNumber raisedTo: anotherNumber  ## Sparkling // e: print(M_E); // π: print(M_PI); // square root: let five = sqrt(25); // logarithm // natural: let one = log(M_E); // base-2: let six = log2(64); // base-10 let three = log10(1000); // exponential let e_cubed = exp(3); // absolute value let ten = abs(-10); // floor let seven = floor(7.8); // ceiling let four = ceil(3.2); // power let eighty_one = pow(3, 4); ## Standard ML Math.e; (* e *) Math.pi; (* pi *) Math.sqrt x; (* square root *) Math.ln x; (* natural logarithm--log base 10 also available (Math.log10) *) Math.exp x; (* exponential *) abs x; (* absolute value *) floor x; (* floor *) ceil x; (* ceiling *) Math.pow (x, y); (* power *) ~ x; (* negation *)  ## Stata scalar x=2 scalar y=3 di exp(1) di _pi di c(pi) di sqrt(x) di log(x) di log10(x) di exp(x) di abs(x) di floor(x) di ceil(x) di x^y  ## Swift import Darwin M_E // e M_PI // pi sqrt(x) // square root--cube root also available (cbrt) log(x) // natural logarithm--log base 10 also available (log10) exp(x) // exponential abs(x) // absolute value floor(x) // floor ceil(x) // ceiling pow(x,y) // power  ## Tcl expr {exp(1)} ;# e expr {4 * atan(1)} ;# pi -- also, simpler: expr acos(-1) expr {sqrt($x)}     ;# square root
expr {log($x)} ;# natural logarithm, also log10 expr {exp($x)}      ;# exponential
expr {abs($x)} ;# absolute value expr {floor($x)}    ;# floor
expr {ceil($x)} ;# ceiling expr {$x**$y} ;# power, also pow($x,$y)  The constants ${\displaystyle e}$ and ${\displaystyle \pi}$ are also available with high precision in a support library. Library: Tcllib (Package: math::constants) package require math::constants math::constants::constants e pi puts "e =$e, pi = $pi"  ## TI-89 BASIC Mathematical TI-89 Notes ${\displaystyle e }$ ℯ  (U+212F SCRIPT SMALL E) ${\displaystyle \pi }$ π  (U+03C0 GREEK SMALL LETTER PI) ${\displaystyle \sqrt{x} }$ √(x)  (U+221A SQUARE ROOT) ${\displaystyle \log_e(x) }$ ln(x)  ${\displaystyle \log_{10}(x) }$ log(x)  ${\displaystyle \log_b(x) }$ log(b, x)  The optional base argument comes first ${\displaystyle \lfloor x\rfloor}$ floor(x)  ${\displaystyle \lceil x\rceil }$ ceiling(x) ${\displaystyle x^y }$ x^y  ## True BASIC FUNCTION floor(x) IF x > 0 THEN LET floor = INT(x) ELSE IF x <> INT(x) THEN LET floor = INT(x) - 1 ELSE LET floor = INT(x) END IF END FUNCTION PRINT "e = "; exp(1) ! e not available PRINT "PI = "; PI LET x = 12.345 LET y = 1.23 PRINT "sqrt = "; SQR(x), x^0.5 ! square root- NB the unusual name PRINT "ln = "; LOG(x) ! natural logarithm base e PRINT "log2 = "; LOG2(x) ! base 2 logarithm PRINT "log10 = "; LOG10(x) ! base 10 logarithm PRINT "log = "; LOG(x)/LOG(y) ! arbitrary base logarithm PRINT "exp = "; EXP(x) ! exponential PRINT "abs = "; ABS(-1) ! absolute value PRINT "floor = "; floor(x) ! floor easily implemented as functions PRINT "ceil = "; CEIL(x) ! ceiling PRINT "power = "; x ^ y ! power END  ## UNIX Shell Works with: ksh93 ksh93 exposes math functions from the C math library echo$(( exp(1) ))      # e
echo $(( acos(-1) )) # PI x=5 echo$(( sqrt(x) ))     # square root
echo $(( log(x) )) # logarithm base e echo$(( log2(x) ))     # logarithm base 2
echo $(( log10(x) )) # logarithm base 10 echo$(( exp(x) ))      # exponential
x=-42
echo $(( abs(x) )) # absolute value x=-5.5 echo$(( floor(x) ))    # floor
echo $(( ceil(x) )) # ceiling x=10 y=3 echo$(( pow(x,y) ))    # power

Output:
2.71828182845904524
3.14159265358979324
2.2360679774997897
1.60943791243410037
2.32192809488736235
0.698970004336018805
148.413159102576603
42
-6
-5
1000

## V (Vlang)

Many more in math module.

import math

fn main() {
x := -1.2345
println("e = ${math.e}") println("pi =${math.pi}")
println("sqrt(4) = ${math.sqrt(4)}") println("log(e) =${math.log(math.e)}")
println("exp(x) = ${math.exp(x)}") println("abs(x) =${math.abs(x)}")
println("floor(x) = ${math.floor(x)}") println("ceil(x) =${math.ceil(x)}")
println("pow(-x, x) = \${math.pow(-x, x)}")
}

## Wren

var e = 1.exp

System.print("e         = %(e)")
System.print("pi        = %(Num.pi)")
System.print("sqrt(2)   = %(2.sqrt)")
System.print("ln(3)     = %(3.log)")    // log base e
System.print("exp(2)    = %(2.exp)")
System.print("abs(-e)   = %((-e).abs)")
System.print("floor(e)  = %(e.floor)")
System.print("ceil(e)   = %(e.ceil)")
System.print("pow(e, 2) = %(e.pow(2))")

Output:
e         = 2.718281828459
pi        = 3.1415926535898
sqrt(2)   = 1.4142135623731
ln(3)     = 1.0986122886681
exp(2)    = 7.3890560989307
abs(-e)   = 2.718281828459
floor(e)  = 2
ceil(e)   = 3
pow(e, 2) = 7.3890560989306


## XPL0

include c:\cxpl\codes;                          \intrinsic 'code' declarations

func real Power(X, Y);  \X raised to the Y power
real X, Y;
return Exp(Y*Ln(X));

real E, Pi;
[Format(4, 16);                                 \places shown before and after .
E:= Exp(1.0);
RlOut(0, E);  CrLf(0);
RlOut(0, Ln(E));  CrLf(0);
CrLf(0);
Pi:= ATan2(0.0, -1.0);                          \Pi is also a defined constant
RlOut(0, Pi);  CrLf(0);
RlOut(0, Cos(Pi));  CrLf(0);
CrLf(0);
RlOut(0, Sqrt(2.0));  CrLf(0);                  \Sqrt is a call to an intrinsic
RlOut(0, Log(100.0));  CrLf(0);
RlOut(0, Ln(Exp(123.456789)));  CrLf(0);
CrLf(0);
RlOut(0, abs(-1234.5));  CrLf(0);               \abs works for both reals & ints
CrLf(0);
RlOut(0, float(fix(1.999-0.5)));  CrLf(0);      \floor   rounds toward -infinity
RlOut(0, float(fix(1.001+0.5)));  CrLf(0);      \ceiling rounds toward +infinity
RlOut(0, Power(sqrt(2.0), 4.0));  CrLf(0);      \sqrt is an inline function and
]                                               \ can be used for both reals & ints
Output:
   2.7182818284590500
1.0000000000000000

3.1415926535897900
-1.0000000000000000

1.4142135623731000
2.0000000000000000
123.4567890000000000

1234.5000000000000000

1.0000000000000000
2.0000000000000000
4.0000000000000000


## Yabasic

print "e     = ", euler
print "pi    = ", pi

x = 12.345
y = 1.23

print "sqrt  = ", sqrt(2)              // square root
print "ln    = ", log(euler)           // natural logarithm base e
print "log   = ", log(x, y)	       // arbitrary base y logarithm
print "exp   = ", exp(euler)           // exponential
print "abs   = ", abs(-1)              // absolute value
print "floor = ", floor(-euler)        // floor
print "ceil  = ", ceil(-euler)         // ceiling
print "power = ", x ^ y, "  ", x ** y  // power
end
Output:
e     = 2.71828
pi    = 3.14159
sqrt  = 1.41421
ln    = 1
log   = 12.1405
exp   = 15.1543
abs   = 1
floor = -3
ceil  = -2
power = 22.0056  22.0056

## Zig

const std = @import("std");

pub fn main() void {
var x: f64 = -1.2345;
std.debug.print("e = {d}\n", .{std.math.e});
std.debug.print("pi = {d}\n", .{std.math.pi});
std.debug.print("sqrt(4) = {d}\n", .{std.math.sqrt(4)});
std.debug.print("ln(e) = {d}\n", .{std.math.ln(std.math.e)});
std.debug.print("exp(x) = {d}\n", .{std.math.exp(x)});
std.debug.print("abs(x) = {d}\n", .{std.math.absFloat(x)});
std.debug.print("floor(x) = {d}\n", .{std.math.floor(x)});
std.debug.print("ceil(x) = {d}\n", .{std.math.ceil(x)});
std.debug.print("pow(f64, -x, x) = {d}\n", .{std.math.pow(f64, -x, x)});
}


## zkl

(0.0).e        // Euler's number, a property of all floats
(0.0).e.pi     // pi, yep, all floats
(2.0).sqrt()   // square root
(2.0).log()    // natural (base e) logarithm
(2.0).log10()  // log base 10
(0.0).e.pow(x) // e^x
(-10.0).abs()  // absolute value, both floats and ints
x.pow(y)       // x raised to the y power
x.ceil()       // ceiling
x.floor()      // floor